Sam,
My guess is that you have a river crossing or dam downstream that you need to burn a breach through. If this is the case, add a feature in the agreestream layer (default layer name in ArcHydro) that goes through the crossing/dam to lower the DEM in a slot through the crossing/dam so that when you fill the DEM you will not fill up the area behind the crossing. This will result in a flow direction grid that reflects the terrain. Through a lake where you don't have a bathymetry surface in the DEM, you have to add an agreestream feature that will burn through that to get a definite flow path.
If you don't have Arc Hydro, you can do some Spatial Analyst to burn in some streams and fix the issue.
Attached is a document I wrote and just updated to add the "Burning Steams" section. I wrote this to preserve for myself and pass on to others how I figured out how do do this process without Arc Hydro. Arc Hydro has some very handy tools and is worth learning if you are doing this repeatedly. The part about burning stream is what you would want to use to possibly address your issue. The document has not been reviewed by others so forgive any bad grammar or spelling.
Hope this helps,
Mark